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Theorem rexalim 2296
Description: Relationship between restricted universal and existential quantifiers. (Contributed by Jim Kingdon, 17-Aug-2018.)
Assertion
Ref Expression
rexalim (x A φ → ¬ x A ¬ φ)

Proof of Theorem rexalim
StepHypRef Expression
1 ralnex 2293 . . 3 (x A ¬ φ ↔ ¬ x A φ)
21biimpi 113 . 2 (x A ¬ φ → ¬ x A φ)
32con2i 545 1 (x A φ → ¬ x A ¬ φ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wral 2283  wrex 2284
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-5 1316  ax-gen 1318  ax-ie2 1365
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1234  df-ral 2288  df-rex 2289
This theorem is referenced by: (None)
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